Let R be a commutative Artinian ring with \(|{\text{Max}}(R)|=n \ge 2\). We show the comaximal graph of R has no cut-sets with more than one vertex. It has exactly a cut vertex if and only if \(R \simeq F\times \mathbb {Z}_2 \times \cdots \times \mathbb {Z}_2\), where F is a field, \(\vert F \vert > 2\) and \(n \ge 3\). It has n cut vertices if and only if R is a Boolean ring.

中文翻译：

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在可交换 Artinian 环的共极大图中切割顶点

令R是一个具有\(|{\text{Max}}(R)|=n \ge 2\)的可交换 Artinian 环。我们展示了R 的共极大图没有超过一个顶点的割集。当且仅当\(R \simeq F\times \mathbb {Z}_2 \times \cdots \times \mathbb {Z}_2\)，其中F是一个场，\(\vert F \vert > 2\)和\(n \ge 3\)。当且仅当R是布尔环，它有n 个切割顶点。